Determine to the nearest tenth the
surface area of a tin can with a radius of eight centimetres and a height of 16
This tin can is a cylinder. So we’ll begin with a sketch of the
tin can. We’re told that the radius of the
tin can is eight centimetres; we’re also told that the height of the can is 16
centimetres. Let’s recall the formula for
finding the surface area of a cylinder.
The formula is two 𝜋𝑟 squared
plus two 𝜋𝑟ℎ. The first part of this formula two
𝜋𝑟 squared gives the area of the circles on the top and base of the cylinder. The second part two 𝜋𝑟ℎ gives the
area of the curved part of the cylinder, which when unfolded forms a rectangle with
dimensions ℎ, the height of the cylinder, and two 𝜋𝑟, the circumference of the
circles on the top and the base.
Let’s substitute the values of 𝑟
and ℎ for the cylinder in this question. The radius of the cylinder is eight
centimetres, so we have two multiplied by 𝜋 multiplied by eight squared for the
first term. The height of the cylinder is 16
centimetres, so we have two multiplied by 𝜋 multiplied by eight multiplied by 16
for the second term.
Now, we’ve been asked for our
answer to the nearest tenth. So we’ll assume we’re allowed to
use a calculator within this question. Evaluating each of the constants
gives 128𝜋 plus 256𝜋. Summing these two terms gives 384𝜋.
Now we need our answer to the
nearest tenth. So we need to go on and actually
evaluate this as a decimal. So using my calculator, we have a
value of 1206.371579. Remember the question has asked us
for the value to the nearest tenth, so I need to round this answer. I also need to include area units
which in this problem are centimetres squared. So we have an answer of 1206.4
centimetres squared for the total surface area of the tin can.